Question
Verify: x3 + y3 = (x + y)(x2 - xy + y2)
Solution
We know that
(x + y)3 = x3 + y3 + 3xy(x + y)
| Using Identity VI
⇒ x3 + y3 = (x + y)3 - 3xy(x + y)
⇒ x3 + y3 = (x + y){(x + y)2 - 3xy)
⇒ x3 + y3 = (x + y)(x2 + 2xy + y2 - 3xy)
| Using Identity I
⇒ x3 + y3 = (x + y)(x2 - xy + y2)
